Chapter 9: The Effect of Catalysed and Uncatalysed Enhancement on the Net Global Air-Sea CO2 Flux.

The Rate of Air-Sea CO₂ Exchange: Chemical Enhancement and Catalysis by Marine Microalgae.

Chapter 9: The Effect of Catalysed and Uncatalysed Enhancement on the Net Global Air-Sea CO₂ Flux.

Note: you may also like to look at the page of animated gif images showing the seasonal cycle of the CO₂ flux and transfer velocity.

9.1 Overview

This chapter presents calculations of the effect of chemical enhancement on the net global air-sea CO₂ flux, both with and without enzyme catalysis, based on the experimental results and theoretical predictions presented in earlier chapters.

At any one location, the unenhanced air-sea CO₂ flux depends on the turbulence at the sea surface (usually parameterised as a function of windspeed), the temperature, and DpCO₂ (for a general introduction, see Section 1.2.1 ). In addition, the chemical enhancement will also depend on the concentration of OH^- (which affects the CO₂ hydration rate -see Section 1.5.1 ), and the degree of catalysis by carbonic anhydrase (which will depend on both the concentration of algae in the microlayer, and their physiological demand for enzyme -see Section 3.2 ). The net global air-sea CO₂ flux is finely balanced and dependent on the intercorrelation between the various parameters, as shown by the preliminary calculations already presented in Section 3.3 . Therefore, large datasets of these parameters are needed to make even a reasonable sensitivity analysis of the effect of chemical enhancement. Using average rather than real data could lead to an entirely misleading result.

Jacqueline Boutin and colleagues at the Laboratoire d'Oceanique Dynamique et de Climatologie (LODYC) in Paris have already carried out such calculations of the effect of uncatalysed chemical enhancement on the net global air-sea CO₂ flux (Boutin and Etcheto 1995, Boutin et al 1997). Therefore it seemed sensible to build on this work using the same datasets as Boutin, particularly as LODYC was also our partner in the ESCOBA programme and have a long experience of using satellite wind and temperature data to predict the transfer velocity (see for example Etcheto and Merlivat 1988). Comparison with the results given by Boutin and Etcheto (1995) and Boutin et al (1997) will also provide a useful check on the new calculations presented here, although the methods and datasets are not identical.

The CO₂ flux due to chemical enhancement is a small fraction of the total net global air-sea CO₂ flux, which is itself a small fraction of the gross regional and seasonal air-sea and sea-air CO₂ fluxes (see Section 1.3 ). Therefore changes to this chemical enhancement effect which seem relatively small locally can make a large difference at the global scale if they are biased towards high or low pCO₂ regions of the ocean. For this reason, to explain the effect of chemical enhancement on the net global air-sea CO₂ flux it is necessary to look in detail at the spatial and temporal variation of each controlling factor and to identify where and when each process is most significant. To help such analysis, a total of 1200 global maps and monthly latitude-band plots were produced automatically by the computer programs described in Section 9.5 , based on many different combinations of calculation options, which are summarised in Section 9.4 . However it would be impossible to show so many plots here in this thesis, and in any case many of them look very similar, so only a select few which seemed particularly revealing are included in figures here. The global average CO₂ fluxes and transfer velocities calculated from each set of calculation options are all presented, however, in tables 9-3, 9-4, and summarised graphically in figure 9-17 .

9.2 Source of Data

Windspeed, Temperature, D pCO₂ and pH datasets were provided by Jacqueline Boutin of LODYC, at a resolution of 1 degree by 1 degree. Chlorophyll datasets were downloaded from the SEAWIFS web page. More details follow:

9.2.1 Windspeed and Temperature

The windspeed data is derived from the ERS1 satellite scatterometer measurements during 1993. Because the windspeed varies significantly on a timescale of a few days, and the dependence of the transfer velocity on the windspeed is highly non-linear, monthly average windspeed data is not sufficient to represent the full variability. Four "weekly" average windspeeds were therefore used for each square degree for each month (so each one actually represents either 7 or 8 days). Each weekly windspeed is itself an average of at least 10 scatterometer measurements. Extrapolations were made to fill the data points for which there were not sufficient measurements (mainly due to cloud cover). Between 50S and 60N the extrapolation was done using adjacent data points along the same latitude (this extrapolation was included in the datasets sent by Jacqueline Boutin). This is not appropriate for the polar regions since missing data might be due to sea ice, so in these regions I extrapolated temporally using the monthly average of valid data for that location. If all four weekly datapoints were missing the location was assumed to be ice-covered and the gas exchange zero.

For further discussion of the application of scatterometer measurements to air-sea gas exchange calculations, particularly the problems of averaging over short timescales, and of converting scatterometer measurements to windspeeds, refer to Boutin and Etcheto (1991, 1997), Etcheto et al (1991), Etcheto and Merlivat (1988).

The sea-surface temperature dataset was also derived from satellite measurements during the same period as the windspeed data. However as sea-surface temperature is much less variable than windspeed, one monthly average value was used for each degree square. There was no missing temperature data.

The plots in figure 9-1 show the average windspeed and the temperature for February (left) and August (right). The method for creating these plots is explained later.

9.2.2 DpCO₂ and pH

Although there are many separate datasets of DpCO₂ derived from ship measurements (see Section 1.3 ), at the time of writing there is still no global seasonal dataset available in a form which is convenient for the purposes of this net global air-sea CO₂ flux calculation. Measurements have been made using many different methods over several decades and the data is arranged in many different formats. Thus, correcting, combining and extrapolating them to produce data for each month and square degree would be a major project in itself, well beyond the scope of this study. Therefore it was much more convenient to use the same source of pCO₂ data as Boutin and Etcheto (1995) which the surface pCO₂ distribution predicted by the Hamburg ocean carbon cycle model created by Maier- Reimer (1993) (see also Kurz and Maier-Reimer 1995). The model predictions for the year 1988 were used on the recommendation of Jacqueline Boutin. This model produces monthly DpCO₂ and pH data on a 2.5 degree grid, which was interpolated by Jacqueline Boutin to a 1 degree grid. Some coastal regions were excluded from the coarser grid -the effect of this is discussed later in section 9.2.4

The following figures derived from this model give an idea of the variation of DpCO₂ and may be helpful for comparison with other models or datasets: Global average monthly DpCO₂: -7.99 ppm, Global average absolute monthly DpCO₂: 25.64 ppm, minimum DpCO₂: -167.3 ppm, maximum DpCO₂ +154.8 ppm.

It must be remembered that such ocean carbon cycle models are very sensitive to their boundary conditions -including the air-sea gas exchange rate itself! When calculating the DpCO₂ used here, the model used the parameterisation of the air-sea gas exchange rate of Liss and Merlivat (1986) (Boutin, personal communication). If instead the model had used the parameterisation of Wanninkhof (1992), or another parameterisation based on the global ¹⁴C budget, which gives higher average transfer velocities, the air-sea pCO₂ differences predicted by the model would be considerably lower because the surface mixed layer would equilibrate faster with the atmosphere.

Moreover recent work has shown that surface pCO₂ is intercorrelated locally with windspeed and chlorophyll on the timescale of just a few hours (see examples in Section 1.3.3 ). For example, strong winds deepen the mixed layer bringing high-CO₂ intermediate water to the surface, whereas algal blooms can decrease pCO₂ dramatically within just a few days. To include the effect of such local intercorrelations in a net global air-sea CO₂ flux calculation would require not only higher resolution datasets, but also that the data for windspeed, chlorophyll, temperature and DpCO₂ were all derived from simultaneous measurements, whereas in this calculation they are derived from several different years! Such simultaneous high-resolution datasets are not yet available on a global scale. Discussion of this issue will be continued in section 10.4. Due to these limitations the results presented here should only be considered as a sensitivity test of the chemical enhancement effect, not as an indication of the real net global air-sea CO₂ flux.

Figure 9-2 shows DpCO₂ and the calculated OH^- concentration for February (left) and August (right). The OH^- concentration has been shown rather than the pH, because this is the factor which affects the uncatalysed chemical enhancement of air-sea CO₂ exchange. Note that contrary to intuition, when the pCO₂ is low and the pH is high, the OH^- concentration is low and vice versa, as can be seen from the summary plots shown at the end of this section ( figure 9-4 ). The reason for this is that water dissociates much more readily at higher temperatures, so both the concentrations of [OH^-] and [H+] are highest in tropical seas. Recall in table 7-1 , how the water dissociation constant K_w increases by a factor of almost 20 as the temperature rises from 0 to 30C! This "K_w effect" dominates over the effect of varying pCO₂ in the ocean.

9.2.3 Chlorophyll

Chlorophyll data were derived from Coastal Zone Colour Scanner satellite measurements averaged over a period of many years. This data is available from the SEAWIFs web page (at the time of making these calculations, the more recent data from the SEAWIFS satellite itself was not available globally for all seasons).

The data is conveniently provided for each month at 1 degree square resolution. However the monthly datasets contain many gaps particularly in the polar regions and also in the central Pacific. I therefore extrapolated across these gaps by taking a moving average of all the valid data points at the same latitude and within +/- 30 degrees longitude. It is necessary to average over so many points both to cover the wide gaps and to avoid extrapolating occasional very high values along the coasts into large areas of the adjacent ocean, whilst the 30 degree restriction avoids extrapolation between, for example, the Atlantic and the Pacific. In some of the global plots which include enzyme catalysis there are a few distinct horizontal stripes which arise from this extrapolation. Also, in the polar seas in winter a sharp cut off can be seen beyond which there is no enzyme effect at all because there was no valid chlorophyll data north or south of that latitude, presumably due to insufficient light.

Figure 9-3 shows chlorophyll plots for February (left) and August (right). In this figure a log scale is used to show the large areas with low but nevertheless significant levels of chlorophyll. However, the original values rather than their logarithms were used for calculating the distribution of enzyme catalysis.

9.2.4 Land and Ocean Area

All locations where there were no valid scatterometer windspeeds for the whole year were assumed to be either land or permanent sea-ice, and these areas were skipped in the calculation. Note the unusual outline of Antarctica and the Arctic ice-cap derived from this method, which can be seen in the plots of average windspeed shown in figure 9-1 . The chlorophyll dataset, which also contained zero for all land areas, was superimposed on the "land" dataset derived from the windspeeds as a check to confirm that these two datasets from different sources were correctly aligned in the computer progam.

Due to the coarser 2.5 degree grid of the Maier-Reimer ocean carbon model, some coastal areas which have temperature and windspeed data do not have DpCO₂ data, as is apparent from white areas in the global plots. Data is missing for the East China Sea, the Japan Sea, the area within the Indonesian archipelago, the Red Sea, the Baltic Sea and most of the Mediterannean. This should not make a significant difference to the calculations of the uncatalysed chemical enhancement, but may be significant in the calculation of the net global air-sea CO₂ flux due to catalysed chemical enhancement, since these coastal areas which cannot be used contain some of the highest chlorophyll concentrations. This will be discussed further later (see Section 9.7.3 )

The area of a square degree at the equator was taken to be 12363.4 km² . This is multiplied by the cosine of the latitude to give the area corresponding to each datapoint, which is used for the calculation of the net global air-sea CO₂ fluxes and global average transfer velocities. The total ocean area calculated this way was found to be consistent with the figure given in UEA-ENV environmental science databook. For the purpose of calculating averages of the transfer velocity and other parameters, the total area of all valid datapoints was calculated for each month and latitude band. These areas are shown in the thickness of the bars in the monthly latitude-band plots such as, for example, those in figure 9-4 . Note how in these plots the area of the polar latitude bands varies seasonally due to sea ice. Slightly lower total surface areas were used for calculating net air-sea CO₂ fluxes, due to the missing coastal regions as noted above.

9.2.5 Summary of input data

The six monthly latitude-band plots in figure 9-4 summarise all the input data. These may be useful later to identify and explain some of the features of similar monthly latitude-band plots of calculated transfer velocities and CO₂ fluxes. The way this type of plot was generated is explained in the summary of the computer programs (see Section 9.5.5 ).

9.3 Calculation Method

9.3.1 Basic calculation of the transfer velocity and chemical enhancement

Calculations were made using both the Liss and Merlivat (1986) and the Wanninkhof (1992) parameterisations of the unenhanced transfer velocity, which have been given earlier (see Section 1.2.12 and figure 1-4 ). The standard form of the Wanninkhof parameterisation, i.e. k_w = 0.31u² (Sc/660)^-0.5, was used even for the chemically enhanced transfer velocity, rather than the amended form with a parameter of 0.304 suggested by Wanninkhof (1992) and used by Boutin and Etcheto (1995), which was calibrated such that the enhanced global average transfer velocity should still match that derived from the global ¹⁴C budget. If I had followed that approach I would have had to recalibrate the formula for every one of the 132 different combinations of calculation options (see Section 9.4 ). Consequently, it would have been very difficult to compare the effect of the various options on the transfer velocity and the net global air-sea CO₂ flux. Moreover, since the global average windspeed derived from this dataset is lower from that used by Wanninkhof to derive his parameterisation, the global average transfer velocity would not match the ¹⁴C figure anyway (as discussed in chapter 6 for the analysis of the laboratory results, and will not be repeated here. The enhancement formula of Hoover and Berkshire (1969) was calculated in full for each weekly windspeed using the pH from the carbon cycle model to derive the [OH^-]. The temperature dependent constants and carbonate system speciation were also recalculated for each grid point.

In contrast, Boutin and Etcheto (1995) and Boutin et al (1997) used a constant pH to determine the carbonate speciation in seawater and to multiply by k_OHK_w to determine the rate of reaction between CO₂ and OH^-, since a preliminary investigation had shown that using a variable pH made little difference to the overall results (Boutin et al 1997, also personal communication). However, Boutin and Etcheto (1997) used the formula for k_OHK_w given by Emerson (1995) which I believe greatly underestimates the reaction rate and is certainly inconsistent with my experimental results (this has already been discussed earlier -see Section 1.5.2 and Section 7.7 ).

Boutin and Etcheto (1995) and Boutin et al (1997) also made the standard assumption that the temperature effect on the Schmidt number and the solubility for CO₂ cancel. The extent to which this assumption is valid has already been demonstrated in figure 7-3 ( Section 7.3 ), which shows the experimentally measured CO₂ transfer rates in normal and acidified seawater as a function of temperature. The line through the transfer velocities for acidified seawater, i.e. without any enhancement, is indeed almost flat, although it curves slightly at the extreme ends of the temperature range. Making this assumption saves considerably on computation time since in their calculation the reaction rates of CO₂ with water and with OH^- were the only temperature dependent constants, which had to be recalculated for each grid point. However, as computer processors become faster, it is now no longer necessary to make such simplifications which might even slightly influence the finely-balanced net global air-sea CO₂ flux calculation.

9.3.2 Multiplying the rate of reaction between CO₂ and OH^- by a factor of six to match the experimental results.

The experimental results from the gas-exchange tank, summarised in Section 7.7 , suggested that the Hoover and Berkshire formula underpredicted the chemical enhancement, and that this underprediction was not a constant proportion but was systematically greater at higher temperatures and lower water pCO₂. Figure 7-12 and figure 7-13 demonstrated that the easiest way to reconcile the complete dataset of measured and predicted data was to increase the CO₂ + OH^- reaction rate used in the prediction (originally taken from Johnson 1982) by a factor of six. This does not necessarily mean that the CO₂ + OH^- reaction rate in seawater is actually that much faster (although this hypothesis should be tested by further measurements), but this is the simplest way to represent the experimental results in one formula. Therefore this was one of the options used in the global flux calculations presented here, and the effect of this option will be discussed specifically in

9.3.3 Use of Rayleigh distribution to split weekly windspeeds

I did not have the data of the standard distribution of the weekly windspeeds which Jacqueline Boutin used to account for the short timescale variation in windspeed (this is discussed in Boutin and Etcheto 1995). Since the transfer velocity is a concave non-linear function of the windspeed, even averaging the windspeed over one week causes an underestimate of both the unenhanced transfer velocity - which is proportionally greater at very high windspeeds - and of the chemical enhancement effect - which is proportionally greater at very low windspeeds. Therefore it was necessary to investigate the effect of using a range of windspeeds in the calculation with the same weekly average as given by the real data. It is well known that the global windspeed distribution approximates well to a Rayleigh distribution (see Wanninkhof 1992). This approximation is unlikely to be valid over the small range of variation found during one week over one square degree, but nevertheless the Rayleigh distribution is a convenient way to investigate the possible importance of such short-timescale variability on the average transfer velocity and net global air-sea CO₂ flux because, unlike the normal distribution, it has only one parameter (the mean), so the standard deviation data is not required. The formula is:

probability (u / u_av ) = (p / 2) * (u / u_av) * exp[ - (u / u_av)² * p / 4 ]
where u = specific windspeed and u_av = average windspeed

Note that this formula for the Rayleigh distribution is not the same as given by Wanninkhof (1992), in which I believe there is a typing error, because the mean of this distribution is not the average windspeed and the integral is not one as it should be in a probability density function. This error was also noted by VanScoy et al (1995).

To make use of this distribution in a net global air-sea CO₂ flux calculation the smooth function must be converted into a histogram of discrete bands. As a compromise between accuracy and computation speed I chose to use 10 such bands, ranging from 0.4 to 4.0 times the average weekly windspeed. The transfer velocities with and without chemical enhancement were calculated for each windspeed band in the normal way. Each one was then multiplied by the probability of the wind being in that band, and totalled to give the weekly average. The probabilities are calculated according to the above formula, multiplied by the width of the band, and by a normalising factor, close to 1, which compensated for the slight change in the total integral caused by dividing a smooth function into rectangular chunks. The step-by-step process is shown in the summary of the computer program, and the validity of this approach is discussed further in the analysis of the results in figure 9-8 shows the various windspeed distributions.

9.3.4 Distribution of Carbonic Anhydrase enzyme catalysis -based on chlorophyll and physiology

In Section 3.2 a physiological model was developed to calculate how a given concentration of carbonic anhydrase (CA) enzyme at the surface of a "typical diatom" would increase its potential growth rate. The model predicted that there would be much more physiological "benefit" from making the enzyme when pCO₂ in the water is low. This prediction was supported both by the experimental results in the gas-exchange tank, reported in chapter 8, and by recent experimental results reported in the literature (see Section 2.3.4 ). So in the global ocean, a higher concentration of enzyme might be expected where pCO₂ is lower, and this might disproportionately increase the influx of CO₂ into the ocean. To test this hypothesis this physiological model was used to determine the distribution of enzyme catalysis used for some of the global flux calculations reported here.

The distribution of carbonic anhydrase in the ocean should be based not only on the physiological model, but also on the distribution of phytoplankton in the ocean, which can be inferred from CZCS chlorophyll data. Mathematically this can be represented by:

[CA concentration] = [CA / cell (based on physiology)] * [cells / litre (based on chlorophyll)]

This should be calculated for each square degree of the ocean for each month, as for the transfer velocity.

It would be possible to find in the literature typical concentrations of cells per litre in seawater, as a function of chlorophyll, and CA per cell in marine phytoplankton. However, it is the CA concentration in the sea surface microlayer, which influences the air-sea CO₂ exchange rate, and this is likely to much higher than in the bulk water, due both to the surface activity of the enzyme itself (see Section 2.4.4 ), and the enrichment of microalgae in the microlayer (see Section 2.4.3 ). Since it is hard to quantify the extent to which organic molecules and living cells are concentrated in the microlayer, and even harder to quantify the extent to which the enzyme produced on external cell walls becomes available to catalyse air-sea CO₂ exchange , the effective concentration of available CA in the microlayer cannot be deduced from existing measurements of CA per cell and cells per litre (these problems have been discussed in Section 3.6 ). Therefore a top-down approach has been used instead, whose reasoning is as follows:

We are interested in the effect of the distribution of CA enzyme on the net global air-sea CO₂ flux, but we cannot yet work out the likely concentration in the microlayer. So we should take a range of global average values for CA concentration in the microlayer which are of the right order of magnitude to significantly influence this CO₂ flux. Firstly we should distribute this enzyme simply according to the chlorophyll distribution, and then apply the physiological model to redistribute the same amount of total enzyme to the regions of the ocean where it provides the maximum benefit to the phytoplankton, and thus see how the effect of the physiology changes the net global CO₂ flux.

However in practice with such a large dataset it is not possible to keep adjusting the arbitrary parameters of the model determining the enzyme distribution to achieve a particular required global average CA concentration. So the actual procedure was the other way around, as follows:

For the distribution according to chlorophyll only, an arbitrary quantity 3 x 10^-13 moles of CA enzyme was assumed to be available per cell, and there were assumed to be an arbitrary number of 10,000 cells per litre in the microlayer per unit of chlorophyll (in m g l^-1) measured by the CZCS. The catalysed CO₂ hydration rate constant due to this concentration of CA enzyme was calculated for each gridpoint for each month according to the formula given in Section 2.4.5 using the same kinetic data as in Section 2.71 and 3.2. These catalysed rate constants were saved to an intermediate data file. This way the global average CA concentration was found to be 0.8308 nM and the global average catalysed CO₂ hydration rate constant was found to be 0.01694 s^-1. Later, in the computations of chemical enhancement of the transfer velocity, the figures from this intermediate data file were multiplied by a scaling factor ("enzyme concentration factor") based on the required global average enzyme concentration. For this chlorophyll-only distribution the five "enzyme concentration factors used were 0.25, 1, 4, 16, and 64, resulting in global average CA concentrations ranging from 0.208nM to 53.172nM mol l^-1 . Thus the final quantity of enzyme is determined by this scaling factor, not by the value of the arbitrary numbers given above.

This computation procedure was used because it minimises the number of calculations of the enzyme kinetic formula, which is complicated and requires several temperature dependant constants. It is not strictly valid, because the enzyme concentration and the catalysed rate constant are not linearly related: as the enzyme concentration rises there are slightly fewer free substrate molecules per enzyme molecule. However this nonlinearity should not be significant at the low enzyme concentrations we are considering here -where the substrate (CO₂ or HCO₃^-) concentration is of the order of 10^-3 - 10^-5 mol l^-1 and the enzyme concentration is of the order 10^-7.5 - 10^-9.5 mol l^-1.

Exactly the same overall computation procedure was applied when the amount of CA per cell was determined by the physiological model rather than fixed arbitrarily as above. So the remaining task here is to explain how the physiological model developed in section 3.2, which told us how much a given concentration of CA at the cell surface would increase the potential growth rate of the cell as a function of pCO₂ and temperature, was adapted to answer the reverse question, i.e., for a given pCO₂ and temperature, what should be the optimum concentration of CA at the cell surface?

This adaptation was based on an iterative "cost-benefit" approach. The increase in cell growth rate due to a given amount of amount of CA at the cell surface was calculated based upon the temperature and carbonate speciation in seawater derived from the data for that gridpoint and month. This "benefit" of increased growth rate was then compared with the physiological "cost" of making CA which was linearly proportional to the amount of CA per cell. The amount of CA per cell was adjusted by an iterative method until the "cost" and "benefit" were equal to within 5%. The procedure was:

1. Set the initial amount of CA per cell at a very low, arbitrary level (10^-19 moles).

2. Calculate the percentage increase in growth rate due to this amount of CA, according to the formula for enzyme at the cell surface given in table 9-1 below:

Enzyme concentration factors were chosen for the two physiological distributions such that the range of values for the global average CA concentrations were identical to those for the chlorophyll only distribution. These scaling factors are of course arbitrary and perhaps unrealistic, but since the point of the exercise is to discern the effect of the physiological distributions on the net global air-sea CO₂ flux, the average concentrations must be the same when comparing the three distributions.

The two plots in figure 9-5 show the distribution of the catalysed CO₂ hydration rate constant due to enzyme distributed according to "low cost" physiological distribution, for the months of February and August. Notice how much of the catalysis is in the coastal regions, where there is most chlorophyll, and that the polar regions are favoured especially due to their low pCO₂, whereas there is very little enzyme in the high-pCO₂ eastern and central equatorial Pacific (the western equatorial Pacific has a lower pCO₂).

9.4 Summary of Calculation Options

Codenames for filenames and figures
The code letters below were combined to create the names of the datafiles used in the computation process as described below, and the same names are also used to identify the maps and plots shown later in this chapter. The codes begin with either k = transfer velocity, or f = CO₂ flux, followed by u = unenhanced, e = enhanced, or d = difference enhanced minus unenhanced, and then followed by the codes for the calculation options. Calculation Options

Use Wanninkhof rather than Liss & Merlivat parameterisation of transfer velocity (code w)

Split weekly windspeeds using Rayleigh distribution (code r)

Multiply OH^- reaction rate by six (code o)

Include enzyme catalysis - using one of three distributions (chlorophyll only, physiology "low cost", physiology "high cost") combined with a concentration scaling factor to reach one of five global average CA concentrations (0.208nM, 0.831nM, 3.323nM, 13.293nM, 53.172nM) (codes: in order of increasing CA concentration: chlorophyll only: g,a,c,e,i "low cost": h,b,d,f,j "high cost": p,m,n,x,y)

Extra letters at end of codes:
q = ratio of two transfer velocities calculated with different options, z = difference of two transfer velocities or two CO₂ fluxes calculated with different options, 1-12 = January to December.
(For q and z, the calculation option against which the comparison is being made is printed within the figure)

Example of filename / figure codes: "fdwro3" would be the map for the CO₂ flux difference (enhanced minus unenhanced) for the month of March, using the Wanninkhof parameterisation, the Rayleigh splitting of weekly windspeeds, and multiplying the CO₂ + OH^- reaction rate by 6.

9.5 Computation method

9.5.1 The scale of the calculation

From the tables of results shown later, it can be seen that there are 132 possible combinations of the various calculation options above, which result in a different net global air-sea CO₂ flux and global average transfer velocity. For each net global air-sea CO₂ flux calculation there are about 45000 gridpoints (180 degrees latitude * 360 degrees longitude, minus 30% which is land). For each gridpoint for each month, there are input data for temperature, D pCO₂, pH, chlorophyll, and four windspeeds (one for each week). This makes a total of about 4.3 million input data values for each net global air-sea CO₂ flux calculation. For each temperature many thermodynamic and kinetic constants must be calculated. The formula of Hoover and Berkshire (1969) (see Section 1.5.3 ) to calculate the chemical enhancement must be applied for each weekly windspeed, or ten times for each windspeed if it is split using the Rayleigh distribution (see procedure in Section 9.5.3 ). In total the results of over 15 billion individual chemical enhancement calculations are summarised in this chapter.

Standard personal computer software packages would not handle so much data at any reasonable speed. Therefore I wrote "QuickBasic" programs to perform this task. These work by opening many input and output data files simultaneously, but only retaining in memory (at any one time) the data for one degree latitude for one month (plus some running totals and averages). The use of plot code lists to control the calculation and plotting options allows both programs to be left to operate automatically overnight, loading and saving hundreds of data files and bitmaps. Even so, the entire operation took several weeks of almost continuous calculation.

9.5.2 Summary of Computer programs

There are two main programs, which will be described in detail below. The first program carries out the basic calculation of the enhanced transfer velocities, whereas the second program computes CO₂ fluxes, transfer velocity ratios and flux differences, and displays this data either as a series of global maps (one for each month) or as a single plot of the averages for each month in each 10-degree latitudinal band, which will hereafter be referred to as a monthly latitude-band plot. Additionally, to aid interpretation of the results, maps or monthly latitude-band plots can be created showing the difference between (or ratio of) CO₂ fluxes or transfer velocities derived using different calculation options. Keeping these two programs separate and saving data files at intermediate stages allows these various maps and plots to be made without unnecessary repetition of the calculation of the enhanced transfer velocities for each set of options, which is the slowest stage of the process. This also enables errors to be detected and corrected easily by enabling plots to be made at intermediate stages of the calculation. For example initially there were some errors in the conversion of such large datasets into the format needed for the main calculation program, such as the loss of the first digit of some of the temperature data for certain gridpoints- but these soon became apparent as strange stripes or patterns in the global maps and the problem could then be rectified.

A separate program was written to calculate the enzyme distribution based on chlorophyll and physiology, as described in Section 9.3.4 . Other short programs were written to convert the original raw data files into a standard format suitable for rapid processing by the main program, and to produce scatter plots showing the relationship between datasets.

9.5.3 Global Flux Calculation program

The summary of the variables and procedures of the main calculation program given in this section, may be useful as a reference for readers who wish to know exactly how the calculations were made. Definitions:

Data file: contains the values for one input or output variable for each gridpoint (total 360*180 gridpoints ) for one month, or in the case of windspeed, for one week. The typical size of each data file (ASCII format) is about 600Kbytes.

Input variables: *Windspeed (four weekly averages for each month), *Temperature, *DpCO₂, *pH, * land (indicates land or permanent sea-ice) *Enzyme catalysis (if required: derived from separate program to make the enzyme distribution based on chlorophyll distribution and physiology)

Output variables: Unenhanced and Enhanced monthly average transfer velocities. Since many calculation options do not affect the unenhanced transfer velocities, these were only saved when different from previous calculations.

Calculation options: as listed above

Kinetic and Thermodynamic Constants: Solubility, Schmidt number, Diffusivity, Carbonic acid dissociation constants (K₁,K₂), Hydration rate constants (CO₂ +H₂O and CO₂ +OH^- ). These are all calculated for CO₂ in seawater, dependant on temperature, according to the formulae given in section 6.2.

Rayleigh Distribution factor: This factor is multiplied by the weekly average windspeed to give the centre of each "band" of the Rayleigh distribution histogram as explained above. There are ten such bands and the factor ranges from 0.4 to 4.0. The use of this factor saves computing time since the probability for each factor only needs to be calculated once at the beginning of the program. For example, a factor "0.8" , which is close to the mode of the distribution, has a much higher probability than factors of either "0.4" or "4.0" which represent the tail ends of the distribution i.e. calm periods and gusts respectively, relative to the average weekly windspeed.

Enzyme catalysis rate constant and concentration factor: The physiological calculation is quite slow as it requires many temperature dependent kinetic and thermodynamic constants and an iterative loop to find the balancing point where the "cost" of making the enzyme equals the "benefit" in increased growth rate, as explained above. Therefore this stage of the calculation was carried out by a separate program, which takes as its input the data files of chlorophyll distribution, sea temperature, DpCO₂ and pH, and saves in an output data file a catalysed CO₂ hydration rate constant. This constant incorporates not only the calculation of how much enzyme was allocated to the gridpoint by the chlorophyll distribution and physiology, but also the effect of the temperature and carbonate speciation of the seawater on the enzyme kinetics. In the main program the catalysis rate constant is multiplied by a scaling factor which adjusts the global average enzyme concentration. It is then added to the rate constant for the uncatalysed reaction before applying the chemical enhancement formula.

9.5.4 Program structure

Note: The beginning and end of loops are shown in bold, optional sections are shown in italic.

Set up arrays for each input and output variable (as above) for each degree longitude.
Calculate array of probabilities for Rayleigh distribution and normalise so total is one.

Main Calculation loop:

Read variables controlling calculation options (as defined above) from datalist
(if reach end of list then end program)

Month loop: (start with January)
Open input and output data files for this month. The name of the output datafiles depend on the calculation options.
Skip first fifteen degrees latitude input data (this is Antarctic icecap)

Latitude Loop: start at 75^o S
Read the values for each variable from the input data files into the arrays, looping through the longitudes dependent on initial data file structure.

Longitude Loop: start at longitude zero (the combination of latitude and longitude now defines a gridpoint).
Is this gridpoint land or permanent sea-ice? If so transfer velocity and flux are zero, skip forward to 35
If in polar regions (<49^o S or > 59^o N) then extrapolate for missing weekly windspeed data using other data for this month. If no valid data assume sea-ice and skip as for (11) (Note Jacqueline Boutin has already extrapolated spatially for missing windspeed data between 50S and 59N).
Calculate kinetic and thermodynamic constants as a function of temperature (formulae in Section 6.2 ).
Calculate carbonate speciation based on D pCO₂ + 360ppm and pH.

Multiply CO₂+OH^- reaction rate by factor of six if this option in specified

Calculate total CO₂ hydration rate (sum of reaction with water and with OH^-)

Add enzyme catalysis if this option is specified, using "catalysis rate constant" (derived from enzyme distribution program) multiplied by an overall "enzyme concentration factor".

Windspeed loop: Start at first of four weekly windspeeds

If not splitting weekly windspeeds:

Calculate unenhanced transfer velocity according to Liss and Merlivat or Wanninkhof formula.
Calculate equivalent stagnant film thickness
Calculate enhancement factor using Hoover and Berkshire formula

Or if splitting windspeeds using Rayleigh distribution:

Rayleigh distribution factor loop (total ten factors between zero and four)
Multiply weekly windspeed by distribution factor
Calculate unenhanced transfer velocity according to Liss and Merlivat or Wanninkhof formula.
Calculate equivalent stagnant film thickness
Calculate enhancement factor using Hoover and Berkshire formula
Multiply unenhanced and enhanced transfer velocities by probability of that factor (taken from array created at start of program)

Loop to next Rayleigh distribution factor:

add up weekly average unenhanced and enhanced transfer velocities

Loop to next weekly windspeed

Calculate monthly average unenhanced transfer velocity and monthly average enhanced transfer velocity for this gridpoint
Multiply monthly average transfer velocities by CO₂ solubility and a factor to convert units from cm hr^-1 to mol m^-2 m atm^-1 yr^-1.
Save enhanced (and unenhanced if required) monthly average transfer velocity(ies) into output data file(s).
Calculate surface area for the gridpoint (12363394000 m² * Cosine of latitude)
Multiply transfer velocity by DpCO₂ and surface area to get CO₂ flux
Add area to total area, transfer velocity to total transfer velocity, flux to total flux

Loop to next longitude going east until reach 360^o.
Calculate running total of average transfer velocity (i.e. total t.v. divided by total area) and total flux and display on screen for observation
Test that each input variable contains a "check" string containing the latitude, and add this check string to output data files.

Loop to next latitude going north until reach 80^o N (beyond this is Arctic icecap)
Close input and output datafiles

Loop to next month

Loop to next main calculation.

This main calculation program runs for about 30 minutes per global yearly calculation using MS QuickBasic in DOS and a P150 processor. When the weekly windspeeds are split by the Rayleigh distribution, it takes about four times longer.

9.5.5 Program to generate global maps and monthly -latitude-band-plots

This program is actually about twice as long as the main calculation program above. However the principal structure, looping through the months, latitudes, and longitudes is very similar, and most of the rest is concerned with plotting graphics, the result of which can clearly be seen from the figures in this chapter. So only the key points will be discussed below:

The program uses the files already created by the main calculation program containing monthly average enhanced and unenhanced transfer velocities for each gridpoint, and combines this data with the DpCO₂ data to calculate CO₂ air-sea fluxes. As for the main calculation program, each time it loops back to the beginning a datalist tells it which input files to open, the names corresponding to a specific set of calculation options. The datalist also specifies whether to make a global map for each month, or a summary monthly latitude-band plot, and what data should be plotted: i.e. the enhanced or unenhanced transfer velocity or CO₂ flux, or the difference or ratio of two such transfer velocities or CO₂ fluxes to compare the effect of different calculation options.

The global maps are plotted using an equal area projection, i.e. the horizontal width of each degree point is proportional to the cosine of the latitude. This enables fluxes in different areas of the ocean to be compared by eye. To maintain the shape of the oceans the globe is split along the continents (similar to the plots presented by Boutin and Etcheto 1995). The plots were made on the QuickBasic output screen and a subroutine taken from a program archive on the internet was used to save them as bitmaps (BMP files) for later inspection and incorporation into other software. The resolution and range of colours is thus limited by the QuickBasic screen set-up.

In the monthly latitude-band plots the colour also corresponds to the CO₂ flux or average transfer velocity or other parameter per unit area, the total area for each latitude band for each month being indicated by the thickness of the bar. The colour scale was usually calculated automatically from maximum and minimum values, but it could be specified in the datalist if necessary. Note that many monthly latitude-band plots which seem very similar at first sight actually have quite different scalebars! Tables of the monthly averages for each latitude band were also saved as text files. These could be re-loaded to make ratio or difference monthly latitude-band plots quickly, or to change the colour scales of the plots, without the need to recalculate from the original large data files.

The program also calculated the net global air-sea CO₂ flux and global average transfer velocity, as shown in the table of results. Note that when average transfer velocities are calculated, the averages are weighted according to the surface area of ocean corresponding to each gridpoint, and excluding sea-ice.

It should be noted, that sea-air fluxes are positive in the plots (both types), whereas they are reported as negative in the tables, and vice versa.

9.6 Results: CO₂ gas exchange without enzyme catalysis

Altogether the results of 132 different net global air-sea CO₂ flux calculations will be presented here, derived from different combinations of the calculation options. To interpret these, it is necessary to consider the simple cases first and look at the effect of the basic options on the underlying unenhanced transfer velocities and CO₂ fluxes, before looking at the results with chemical enhancement and then with enzyme catalysis.

Table 9-2 summarises the results for the net global air-sea CO₂ fluxes and global average transfer velocities, both due to diffusion only, and due to enhancement by uncatalysed chemical reaction. The figures for reaction should be added to the figures for diffusion to give the total flux or transfer velocity. Percentage increases are also given showing the effect of reaction as a proportion of the equivalent figure for diffusion-only. For comparison, the results published in Boutin et al (1997) are included, as is the global average transfer velocity derived from the Carbon-14 budget. Note that the data above are also included in the graphs summarising the effect of enzyme catalysis ( figure 9-17 ), which will be discussed later ( Section 9.7.1 ).

9.6.1 Gas exchange rate and air-sea CO₂ flux without chemical enhancement

To interpret these results, we need to see where and when in the ocean most of the gas exchange due to diffusion is taking place. The plots in figure 9-6 show the unenhanced transfer velocity (left) and CO₂ air-sea flux (right) for the months of February (top) and August (centre), and the summary plot for the whole year (bottom). These plots should be viewed in conjunction with the equivalent plots for the controlling factors wind, temperature and D pCO₂, figure 9-1 and figure 9-2 shown earlier.

It can be seen that both the transfer velocities and air-sea CO₂ fluxes are greatest in the winter polar seas. Although the highest transfer velocity is in the Southern Ocean due to the strong winds, the highest air-sea CO₂ flux is in the north-west Atlantic and, to a lesser extent in the north-west Pacific, for it is here, in winter, that the pCO₂ is lowest. However in the summer it is in these same regions that the reverse sea-air CO₂ flux is highest, because the pCO₂ has risen with the water temperature, and there is a little more wind than in the equatorial seas. The global average transfer velocity is about half of that derived from the ¹⁴C budget but the net global air-sea flux is 1.9 Gt C yr^-1, in agreement with most recent estimates (e.g. Sarmiento and Sundquist 1992, see also D pCO₂ data is derived was calibrated using the Liss-Merlivat parameterisation to define its sea-surface boundary condition (see Section 9.2.2 ), so it is not surprising that using this formula results in a more realistic net global air-sea CO₂ flux than using the faster gas exchange rate derived from the ¹⁴C budget.

9.6.1.1 Effect of using Wanninkhof parameterisation

We then consider the effect of using the Wanninkhof rather than the Liss and Merlivat parameterisation of the transfer velocity. The net global air-sea flux is 76% higher and the global average transfer velocity is 74% higher, but the latter is still only 5.32 x10^-2 mol m^-2 m atm^-1 yr^-1, whereas we might expect it to be closer to 6.2 x10^-2 mol m^-2 m atm^-1 yr^-1, as predicted by the global ¹⁴C budget from which this parameterisation is derived (see Wanninkhof 1992). Boutin and Etcheto (1995) also noted a similar anomaly and explains that the global average windspeed used in her dataset derived from satellite scatterometer measurements in 1992-23 was only 7.12 ms^-1, whereas that used by Wanninkhof (1992) to derive his parameterisation was 7.4 ms^-1. My own calculation of the average windspeed matched that of Boutin, who states that this is also consistent with other recently measured datasets. As both parameterisations are non-linear with respect to windspeed, the relative difference in the average transfer velocity is greater than the relative change in the average windspeed.

The monthly latitude-band plots in figure 9-7 compare the two parameterisations, showing the ratio of the transfer velocities (left) and the difference of the CO₂ fluxes (right).

The transfer velocity ratio is greatest both in very calm seas (such as just south of the equator in March and just north of the equator in October) and in stormy polar seas, whereas it is lowest at average windspeeds. This is to be expected, as the two parameterisations differ most at both extremes of the windspeed range (see figure 1-4 ). Although the CO₂ flux difference is much greater in the northern polar winter, the mid-latitudes are also significant due to their larger surface area (indicated in the plots by the width of each block).

9.6.1.2 Effect of Rayleigh distribution

We now consider the effect of splitting the weekly windspeeds with the Rayleigh distribution. This increases the average transfer velocity by 16.7% when using the Liss and Merlivat parameterisation and by 24.7% - when using the Wanninkhof parameterisation. This is because the effect of using the Rayleigh distribution is to create more extreme windspeeds (both calms and gusts). Both parameterisations, but especially the quadratic formula, are concave non-linear functions which allocate relatively higher transfer velocities to extreme than to average windspeeds (see figure 1-4 ). The net global CO₂ fluxes are increased by similar proportions.

The Rayleigh distribution was applied, as already explained, because I had data only of weekly average windspeeds rather than individual measurements. Boutin et al (1997), who had the original data, used the standard deviation of the weekly windspeeds to account for short-timescale variability. The figures in table 9-2 show that unenhanced global average transfer velocity and net global air-sea CO₂ calculated by Boutin et al (1997) are both about half way between my equivalent figures calculated with and without the Rayleigh distribution. This to be expected, because the variability over one square degree within one week is likely to much less than the variability of global windspeeds which is well represented by the Rayleigh distribution. So if the weekly average windspeed is used the proportion of extreme winds and hence the average transfer velocity will be underestimated, but if the Rayleigh distribution is applied to split weekly average windspeeds the proportion of extreme winds and hence the transfer velocity will be overestimated. When the original data is used the answer falls somewhere between these two - as observed. Note that the global average transfer velocity derived from the ¹⁴C budget also lies between the figures calculated here using the Wanninkhof parameterisation with and without the Rayleigh splitting of weekly windspeeds, despite the average windspeed being lower than used by Wanninkhof (1992), as noted above.

This analysis is supported further by the figure 9-8 which shows the actual windspeed distributions calculated from the whole dataset. To make the frequency distribution curves the data from each gridpoint (or 10^o latitude band average as in the summary plots), weighted according to the sea surface area, was grouped into 0.5 ms^-1 windspeed bands. Note that the area under all the curves is one and they all have the same mean -indicated by the global average line.

If we assume that the smooth Rayleigh curve (pink) represents the real windspeed distribution, then it is clear that the distribution of weekly average winds (blue) is too narrow and peaked. The monthly average winds are even more bunched towards the mean, but not so badly as the 10^o latitude band average monthly winds. Note that this latter distribution is spiky because in one year there are only 16*12 = 192 values divided between 24 windspeed bands. However, when the weekly windspeeds are each redistributed according to the Rayleigh formula the resulting overall distribution (green line) is too flat. The sharp peak at about 2.5 ms^-1 is an artefact of the method of splitting the Rayleigh distribution into 10 bands (as described earlier) but when the effect of using various numbers of bands was tested, neither a smaller nor a larger number of bands produced a better-shaped distribution overall.

The monthly latitude-band plots in figure 9-9 show the effect of Rayleigh splitting of weekly winds on the spatial and temporal distribution of unenhanced Liss and Merlivat transfer velocities and air-sea CO₂ fluxes - as before the ratio of the transfer velocities is on the left and the difference of the CO₂ fluxes is on the right.

In figure 9-9 , as in figure 9-7 , the ratio is greatest just south of the equator in March and just north of the equator in October, due to very light winds, and the difference plots "fuwz" and "furz" are similar. However "kurq" is different from "kuwq", as here the ratio of transfer velocities is not particularly high in the polar seas, as it was when comparing the two parameterisations. The effect on the CO₂ flux is still greatest in these regions, due to the large DpCO₂ and high winds.

9.6.2 Effect of uncatalysed chemical enhancement

To see the effect of various calculation options on the chemical enhancement, it is more instructive to consider the difference of the enhanced minus unenhanced transfer velocity or CO₂ flux, rather than the total, in other words the extra gas exchange due to the chemical reaction pathway. Hence the figures in the summary table 9-2 and the plots which follow show the transfer velocity or air-sea CO₂ flux due to chemical reaction only.

The six plots in figure 9-10 , show the difference between enhanced and unenhanced transfer velocities (left) and CO₂ fluxes (right) for the case of the Liss and Merlivat parameterisation with the Hoover and Berkshire formula, for February (top), August (centre), and for the whole year (bottom).

The critical point to note is that chemical enhancement is most significant in the tropical oceans, mainly due to the effect of temperature: the rate of reaction of CO₂ with water is much faster at high temperatures, in tropical regions of the oceans, where the surface water pCO₂ is generally high due to the temperature driven "solubility pump" (see introduction Section 1.1.3 ). The average windspeed in the tropical oceans is also lower than in the mid-latitudes and polar oceans, and the reaction pathway for air-sea CO₂ exchange is more important at low windspeeds. Therefore the chemical enhancement effect is most pronounced in regions where there is a net flux of CO₂ from the sea to the air, and so although it increases the global average transfer velocity, it decreases the net global air-sea CO₂ flux.

The data in table 9-2 shows that for this basic case (Liss and Merlivat parameterisation without Rayleigh distribution or faster OH^- reaction) chemical enhancement increases the global average transfer velocity by 5.3% (to 3.217 x10^-2 mol m^-2 m atm^-1 yr^-1). The equivalent increase given by the figures of Boutin et al (1997) is 6.9% (to 3.56 x10^-2 mol m^-2 m atm^-1 yr^-1). The lower figure calculated here is probably due to the use of weekly average windspeeds in this calculation, since averaging reduces the proportion of very low windspeeds where chemical enhancement is greatest (see also next section). The equivalent figure for the net global air-sea CO₂ flux, shows a decrease of 1.9%, agreeing with the decrease of 2.0% calculated by Boutin et al (1997).

Notice also the seasonal variation: the greatest enhancement of the transfer velocity in February is in the Indian Ocean where the windspeed is particularly low, whereas in August the effect is more significant in the north Atlantic and north Pacific, which in the summer are a source of CO₂ to the atmosphere. The transfer velocity plot for July (not shown here) was found to be very similar to the equivalent map shown in the paper of Boutin and Etcheto (1995).

In figure 9-11 , the scatterplot on the left shows the same data for the chemical enhancement of the transfer velocity (every eighth point of the global yearly dataset is included) as a function of pCO₂ (horizontal axis) and temperature (colourscale), confirming that most of the enhancement is in warm high-pCO₂ regions. The equivalent scatterplot of the monthly average windspeed is shown on the right (including every fourth point) shows how these regions tend to have lower winds. Remember however that the pCO₂ data is derived from a carbon cycle model which is not based on the same windspeed dataset, so small scale spatial and temporal intercorrelations between windspeed and pCO₂ will not be shown.

9.6.3 Effect of Rayleigh splitting of weekly winds on chemical enhancement

When the weekly windspeeds are split using the Rayleigh distribution the global average enhanced transfer velocity is 3.807 x10^-2 mol m^-2 m atm^-1 yr^-1(see table 9-2 ), now greater than the figure of Boutin et al (1997), which again supports the conclusion in section 9.6.1.2, that the best estimate should lie somewhere between the figures calculated with and without the Rayleigh splitting.

However when the net global sea-air CO₂ flux is calculated with the Rayleigh windspeeds, the extra CO₂ flux due to chemical enhancement is reduced to only 1.0% of the total, i.e. applying the Rayleigh distribution increases the net air-sea CO₂ flux. To understand why this might be, we should look at the spatial and temporal distribution of the chemical enhancement. The maps in figure 9-12 show the transfer velocity (top left, kdr8) and the air-sea CO₂ flux (top right, fdr8) for the month of August calculated with the weekly windspeeds split by the Rayleigh distribution. The summary monthly latitude-band plots show both the ratio (centre left, figure code kdrq) and the difference (centre right, figure code kdrz) of the transfer velocities calculated with and without this option, and the difference of the CO₂ fluxes (bottom left, figure code fdrz). The scatterplot (bottom right) shows the transfer velocity due to reaction calculated with the Rayleigh distribution option as a function of pCO₂ and temperature as before.

From the ratio plot kdrq, it is clear that the relative increase of the chemical enhancement due to applying the Rayleigh distribution to the weekly windspeeds is greatest in the windiest regions of the world -particularly in the southern ocean. The transfer velocity difference plot kdrz, or a comparison of the maps kdr2 and kdr8 with those shown earlier kd2 and kd8, shows that the absolute effect, although positive everywhere, is greatest in the mid-latitudes. This make sense, since chemical enhancement is greatest at low windspeed. In the tropics the windspeeds are already low so spreading them out with the Rayleigh distribution will not make much difference, whereas in the polar seas the winds are generally too high and the temperatures too low for significant enhancement even during the calmest band of the distribution. The flux difference plot fdrz shows that in summer these mid-latitude regions are sources of CO₂ to the atmosphere, but in winter they are sinks.

Comparison of the scatterplot with the previous scatterplot of transfer velocity due to reaction (fig 9-11) shows that the main effect of the Rayleigh distribution is to push up the datapoints corresponding to medium sea-surface temperatures (green), for most of which the DpCO₂ is negative. Hence the overall effect is to reduce the net sea-air CO₂ flux due to chemical enhancement by 39%.

9.6.4 Effect of Wanninkhof parameterisation on chemical enhancement

The underlying unenhanced transfer velocities are much higher using the quadratic formula of Wanninkhof (1992), and hence the chemical enhancement is generally much lower. Without the Rayleigh distribution, chemical enhancement adds only 1.7% to the global average transfer velocity, and subtracts only 0.6% from the net global air-sea CO₂ flux, as can be seen from
table 9-2 .

The maps in figure 9-13 show the transfer velocity (kdw8, left) and CO₂ flux (fdw8, right) due to chemical enhancement using the Wanninkhof parameterisation (and no Rayleigh splitting), for the month of August. Compared with the equivalent Liss and Merlivat maps kd8 and fd8 shown earlier in figure 9-10 , the enhancement is concentrated even more in the tropics (note that the colourscales here are different from kd8 and fd8). To aid comparison of the two parameterisations, plots of the ratio of the transfer velocities due to reaction only (kdwq, left), and the difference of the CO₂ fluxes (fdwz, right), are also shown in figure 9-13 . Note that the ratios (Wanninkhof / Liss and Merlivat) are all less than one, and smallest in the polar seas. The colourscale for fdwz was forced to be the same as for the other flux difference plots fdrz and fdwrz above, consequently a few blocks are off the negative end of the scale and appear white. The pattern, like that of fdr, reflects the underlying D-pCO₂ distribution, but because the CO₂ fluxes due to chemical enhancement are smaller with the Wanninkhof parameterisation, the colours are reversed.

Perhaps coincidentally, the net global air-sea CO₂ flux due to chemical enhancement calculated with the Rayleigh splitting of weekly windspeeds is almost the same when the Wanninkhof rather than the Liss and Merlivat parameterisation is used to calculate the transfer velocities. However, in this case, the net sea-air CO₂ flux due just to chemical reaction becomes 10% greater when the Rayleigh splitting is applied. The plots kdwrz and fdwrz in figure 9-14 show for the Wanninkhof parameterisation the same differences (transfer velocity and CO₂ flux with and without Rayleigh distribution option), with the same colourscales, as for the Liss and Merlivat parameterisation in figure 9-12 . From these, it is clear that the increase in transfer velocity in the mid-latitudes is much weaker in this case, and the tropical regions, which are a source of CO₂ to the atmosphere, dominate.

9.6.5 Effect of increasing rate of reaction of CO₂ with OH^- by a factor of six

The calculations of chemical enhancement reported above all include the reaction of CO₂ with OH^-, and the concentration of OH^- is varied according to the pH from the Hamburg carbon cycle model, rather than assuming constant pH as in the calculation by Boutin (1995). However there is no discernible bias of the chemical enhancement effect towards low pCO₂ regions, as predicted by Keller (1994) and discussed earlier in this thesis, because the temperature effect on K_w has a much greater effect on the distribution of OH^- in the ocean than the variation in water pCO₂. This has already been demonstrated by the global maps of the OH^- distribution (see Section 9.2.2 ). Keller (1994) did not observe this effect since he used a constant temperature throughout. In his examples he also took a much wider range of pCO₂ than is found in the real ocean, due to a mistaken interpretation of the gross air-sea CO₂ flux (see Section 1.3.8 ). Finally Keller (1994) used a higher rate of reaction between CO₂and OH^-than the figures of Johnson (1982) used so far in this calculation.

Now we investigate the effect of increasing the rate of reaction between CO₂ and OH^- by a factor of six, not because this is probably the correct reaction rate, but because this is the simplest way to represent the experimental results from the gas-exchange tank presented in chapter 7, as explained earlier ( Section 7.7 ). The maps in figure 9-15 show the transfer velocity due to chemical enhancement using this faster CO₂+OH^- reaction rate. Four different months are shown to give an idea of the seasonal variation.

The colourscale used for the transfer velocity plots in figure 9-15 is the same as on the maps kd2 and kd8 shown in figure 9-10 , which showed the basic case with a normal CO₂ + OH^- reaction rate, allowing easy comparison. It can be seen that with the faster OH^- reaction rate the chemical enhancement is both more intense and spreads further into the mid-latitudes. The May and November plots (not shown before) show the importance of the Indian Ocean and Eastern Pacific. Note that the grey ocean areas (the same colour as land) are off the high end of the colourscale.

Figure 9-15 also shows maps of the fluxes due to chemical enhancement with faster CO₂+HO- reaction rate for February (fdo2, bottom left) and August (fdo8, bottom right). Again the fluxes are noticeably greater, particularly in the mid-latitudes.

Figure 9-16 shows a plot of the ratio of the transfer velocities due to chemical enhancement, comparing the normal and the fast CO₂ + OH^- reaction rate (kdoq, left) and a plot of the difference of the corresponding CO₂ fluxes (kdoq, right).

It can be seen that the ratio is fairly constant (1.5-1.9) except for a few high values in the polar regions in winter (up to 2.3), but these are relatively insignificant in the net global sea-air CO₂ flux due to chemical enhancement. Apart from these polar regions, the plot fdoz is similar in pattern to the basic case plot fd. This indicates that the reaction of CO₂ with OH^- just supplements the effect of the direct reaction of CO₂ with water, increasing the sea-air CO₂ flux more than the air-sea CO₂ flux.

The overall effect of increasing the CO₂ + OH^- reaction rate by a factor of six is to increase the global average transfer velocity due to chemical enhancement by an extra 70%, and to increase the net global sea-air CO₂ flux due to chemical enhancement by 49%, when using the Liss and Merlivat parameterisation (se figures in table 9-2 ). The relative effects are even greater for the Wanninkhof parameterisation: 85% and 71% respectively, although the actual changes in the global average transfer velocity and net global air-sea CO₂ flux are smaller.

When the weekly winds are split by the Rayleigh distribution then the effect of the faster CO₂ + OH^- reaction rate on the average transfer velocity due to enhancement drops to 58% and 75% for the Liss and Merlivat and Wanninkhof parameterisations respectively, although the actual increase is greater. However in this case the effect is more widely distributed across the ocean, and hence includes more mid-latitude regions whose air-sea CO₂ flux cancels the sea-air CO₂ flux in the tropics, so the effect of the faster OH^- reaction on the global air-sea CO₂ flux is smaller: 26% and 50% for the Liss and Merlivat and Wanninkhof parameterisations respectively.

9.7 Results including catalysis by Carbonic Anhydrase Enzyme

9.7.1 Discussion of global average effects of enzyme catalysis

All the global average transfer velocities and net global air-sea CO₂ fluxes, including all the combinations of calculation options, are summarised in the four large tables 9-3a, 9-3b, 9-4a, 9-4b. As before, the figures for "diffusion only" should be added to those for catalysed or uncatalysed reaction to give the total fluxes or transfer velocities for each scenario. The figures for the catalysed reaction include the uncatalysed reaction also, as the various reaction pathways compete with each other for the same substrate (CO₂ or HCO₃^-), and also with the diffusion transfer, and therefore their fluxes are not additive. This also true for diffusion compared to reaction, but it is easier to see the effect of the reaction when the diffusion-only figure is subtracted from the total.

Before looking at plots showing the detailed distribution of the CO₂ fluxes and transfer velocities due to enzyme catalysis, we will consider the overall effect of increasing the enzyme concentration and varying its distribution. This is more easily seen in the summary graphs in figure 9-17 , showing all the net global air-sea CO₂ fluxes (top) and global average transfer velocities (bottom) (as in tables 9-3a, 9-3b, 9-4a, 9-4b) as a function of increasing average enzyme concentration.

There are four distinct sets of curves: at the bottom is the Liss and Merlivat parameterisation, above it the Liss and Merlivat with the Rayleigh distribution applied to the weekly winds, above that the Wanninkhof parameterisation, and above that the Wanninkhof with the Rayleigh distribution applied to the weekly winds. Each set of six curves can be subdivided into three groups of two, corresponding to the chlorophyll-only enzyme distribution, the "low cost" physiological distribution, and the "high cost" physiological distribution. The two lines in each pair correspond to the normal OH- reaction rate, and the OH^- reaction rate multiplied by a factor of six. The "diffusion only" data is shown by a straight baseline (yellow) for each set of curves. The origin of each line (i.e. at zero enzyme concentration) shows the "uncatalysed" data, which has already been discussed in the previous sections. To distinguish the lines at low enzyme concentrations more clearly, the origin of each set of lines has been magnified in the small plots on the right of each graph.

The first point to note is that the net global air-sea CO₂ flux is increased by adding any amount of enzyme, whichever of these three distributions is chosen, whereas it was always reduced by the uncatalysed chemical enhancement. This is because even the basic "chlorophyll only" distribution is biased towards colder, lower pCO₂ regions of the ocean, so the enzyme catalysis is enhancing the air-sea CO₂ flux more than sea-air CO₂flux. This is shown by the two scatter plots in figure 9-18 . On the left is the distribution of chlorophyll as a function of pCO₂ and temperature (every fourth point is shown). On the right is the distribution of the transfer velocity due to catalysed chemical reaction only (i.e. the uncatalysed enhancement has been subtracted, the calculation code is kdc - kd).

Although the effects of higher temperatures and lower windspeeds in tropical regions have pushed up the points on the right hand, high-pCO₂ side of the scatterplot of transfer velocity due to catalysed reaction, compared to the chlorophyll scatterplot, nevertheless on average the balance still tips slightly towards the left hand, low pCO₂ side of the transfer velocity scatterplot, and thus the net CO₂ flux due to enzyme is from the air to the sea.

A uniform distribution of enzyme is so unrealistic that it has not been applied here, however if this calculation were done we might expect the reverse effect on the net global air-sea CO₂ flux, since enhancement is favoured at the lower windspeeds and higher temperatures of tropical high pCO₂ regions as explained before. On the other hand the temperature dependence of the catalysed reaction rate is not so strong as for the uncatalysed reaction due to its lower activation energy (see Section 2.7.2 ), so the net CO₂ flux due to uniformly distributed enzyme would be quite finely balanced, perhaps close to zero.

On the main graphs a polynomial curve fit has been used to join the data from each set of calculations, which were made for 0, 0.21, 0.83, 3.3, 13.3, and 53.2 nM average enzyme concentration as explained in Section 9.3.4 . It is clear that as the average enzyme concentration increases, the curves begin to level off so that the effect per mole of enzyme is less. This is not due to enzyme kinetics, because the enzyme concentration would have to be much higher before the substrate was sufficiently scarce in relation to the enzyme to cause such a levelling off. For this reason the enzyme kinetics and the distributions were not recalculated for the different enzyme concentrations (as explained in the Section 9.3.4 ). The levelling off must therefore be intrinsic to the enhancement formula of Hoover and Berkshire (1969) and can be explained by a competition between diffusion and reaction in the sea-surface microlayer. This has already been discussed in Section 7.6.3 with relation to transfer velocities measured in the tank with added bovine enzyme, where a similar levelling-off was observed with increasing enzyme concentrations. Of course, in the real world, if the transfer velocity was that much faster, the DpCO₂ would also decrease due to faster equilibration with the atmosphere, so an even greater levelling off should be expected in the graph of net global air-sea CO₂ flux as a function of enzyme concentration.

Now we should compare the three distributions of enzyme. It is obvious from the graphs that varying the distribution has a much greater effect on the net global air-sea CO₂ flux than on the global average transfer velocity -which is to be expected since the main effect of the physiological distributions is to place more of the enzyme in low pCO₂ regions. For a given global average enzyme concentration the net global air-sea CO₂ flux due only to catalysed reaction is about 4.6 times higher using the "high cost" physiological distribution compared to the "chlorophyll only" distribution, when using the basic Liss and Merlivat parameterisation without Rayleigh splitting. The "low cost" physiological distribution is less selective, so the equivalent ratio for this is about 1.86.

The difference between the two physiological distributions is made clear by the two scatterplots in figure 9-19 which show the amount of carbonic anhydrase per cell for the two physiological distributions, as a function of pCO₂ and temperature (one in every ten points is included). To get the amount of enzyme in each gridpoint, this CA per cell would be multiplied by the chlorophyll and a scaling factor as explained in Section 9.3.4 .

These shape of the distributions are similar to the 3D graph (increased growth rate of a typical diatom due to CA at the cell-surface as a function of pCO₂ and temperature, figure 3-2 ) based on the physiological model developed in Section 3.2 . However, here the real range of temperature and pCO₂ in the ocean is clear. Although there is a clear bias towards low pCO₂, this is partially compensated by the bias towards higher temperatures which, on average, favours the high pCO₂ end of the dataset. So although CA per cell is negatively correlated with pCO₂, if the temperature effect were much greater, the correlation would become positive.

The effect of raising the "cost" of making each mole of CA is to cut off the lower part of the distribution, where the "benefit" of making enzyme is below the cost threshold discussed in the methods section. In this "high cost" scenario nearly all of the enzyme is distributed to low pCO₂ regions where the net flux is from the air to the sea, and therefore it has a much greater effect on the net global CO₂ flux.

Returning to the main graphs in figure 9-17 , it can be seen that as the concentration of enzyme increases, the global average transfer velocity calculated with the "low cost" physiological distribution rises slightly above that calculated using the "chlorophyll-only" distribution. This is because the effect of the physiological distribution is to place the enzyme where it is more effective, and hence the average catalysed hydration rate constant per mole of enzyme is 6.6% higher. These ratios have already been discussed in the Section 9.3.4 , and are listed in table 9-1 .

The figures in table 9-1 show that the average catalysed hydration rate constant per mole of enzyme is 36.2% higher for the "high cost" distribution compared to the "chlorophyll-only" distribution. It is curious then, that the global average transfer velocity calculated with the "high cost" distribution drops significantly below that calculated with the "chlorophyll only" distribution as the enzyme concentration increases. This can be explained by looking at the plots of spatial and temporal variability of the "high cost" distribution, which show that in this case much of the enzyme is concentrated in just a few areas of the ocean where the chemical enhancement will be very high. From the overall flattening of the curves of global average transfer velocity and net air-sea CO₂ flux at higher enzyme concentrations, it has already been concluded that as the CO₂ hydration rate is increased, the enhancement per mole of enzyme decreases, due to competition between reaction and diffusion across the microlayer. This effect will also apply to each individual gridpoint in the dataset. Therefore, if much of the enzyme is concentrated in just a few gridpoints, this competition effect will become more significant at lower global average enzyme concentrations and the flattening of the global average transfer velocity curve will occur sooner, as observed.

The effect of increasing the CO₂ + OH^- reaction rate by a factor of six, which represents the best fit to my experimental results from the gas exchange tank, as explained earlier, can be seen by the gaps between pairs of almost parallel curves. However it is clear that as the enzyme concentration increases, these gaps decrease for the "chlorophyll only" and "low cost" physiological distributions, whereas they become wider for the "high cost" physiological distribution. The reduced effect of the OH^- reaction at high enzyme concentrations can be explained by a similar "competition effect" between the enzyme-catalysed and the OH^- CO₂ hydration / dehydration reaction pathways. However in the case of the "high cost" physiological distribution, most of the enzyme is concentrated in low-pCO₂ waters. Therefore competition from enzyme reduces the extra air-sea flux due to the faster CO₂ + OH^- reaction rate, but not the larger extra sea-air flux due to this faster reaction. The difference between the two, which is the net effect shown as the gap between the curves, is therefore increased by competition from the enzyme.

We should also compare the two parameterisations of the transfer velocity. Adding 13.3nM enzyme distributed according to chlorophyll only increases the net global air-sea CO₂ flux calculated using the Liss and Merlivat parameterisation (without Rayleigh splitting) by 102.6 Mt C yr^-1, or 5.5% of the total, whereas the equivalent figure for the Wanninkhof parameterisation is only 54 Mt C yr^-1, or 1.7% of the total. The difference in the effect on the global average transfer velocity is not quite so dramatic: the equivalent figures are 0.595 mol m^-2 m atm^-1 yr^-1 (18.5%) and 0.441 mol m^-2 m atm^-1 yr^-1 (8.2%) respectively. The explanation is the same as before for uncatalysed chemical enhancement: the unenhanced transfer velocities are higher with the Wanninkhof parameterisation, and hence chemical enhancement is lower. This is particularly important in the windier low pCO₂ regions, and hence using the Wanninkhof parameterisation reduces the extra air-sea flux of CO₂ due to added enzyme in the mid-latitudes and polar seas more than it reduces the extra sea-air flux in the tropics. However, from the graphs it is clear that this difference between the two parameterisations is not so great when the enzyme is distributed according to either of the two physiological distributions. This may be because the physiological distributions favour the medium-windspeed low-pCO₂ regions, whilst removing enzyme from both the high-pCO₂ tropics and the very cold polar seas, and at medium windspeeds the two parameterisation curves are closer than they are at either high or low windspeeds (see figure 1-4 ).

Finally we should consider the effect of splitting the weekly windspeeds using the Rayleigh distribution. The greater effect of Rayleigh splitting on the baseline unenhanced CO₂ flux and transfer velocity for the Wanninkhof parameterisation, compared to the Liss and Merlivat parameterisation, has already been explained earlier. So here we should compare the shapes of the curves with and without Rayleigh splitting of weekly windspeeds. Mostly these curves are almost parallel so there is not generally any great influence on the increased air-sea CO₂ flux or global average transfer velocity due to enzyme-catalysed reaction. The exceptions are that Rayleigh splitting increases the effect of enzyme catalysis on the net global air-sea CO₂ flux when using the "chlorophyll-only" distribution and the Wanninkhof parameterisation, and that it also increases the "competition effect" on the global average transfer velocities calculated with the "high cost" physiological enzyme distribution, as discussed above.

9.7.2 The spatial and temporal variability of enzyme catalysis

There has already been some speculation above about the spatial and temporal variability of enzyme catalysis in the previous section discussing the global average figures. We now look at the maps and plots showing the distribution of catalysed chemical enhancement in more detail.

We will first look at the effect of increasing the global average enzyme concentration. The six plots in figure 9-20 show the transfer velocity (left) and CO₂ flux (right) due to chemical enhancement only (both catalysed and uncatalysed) for the "chlorophyll only" distribution during the month of August. The concentration of enzyme increases from zero at the top (these two maps have been shown before in figure 9-10 ) to 0.83nM in the centre and 3.32nM at the bottom. The three transfer velocity plots share the same colourscale, as do the lower two flux plots. Note that grey patches in the sea, and occasional white spots (where not ice) are off the positive and negative ends of the colourscales respectively.

It is clear that adding the enzyme extends the region where there is significant chemical enhancement, into the higher latitudes both north and south of the tropics. It increases the transfer velocity most in the coastal regions where chlorophyll concentrations are high, especially in the north Atlantic and north Pacific, where in these maps it is summer . From the flux maps it is clear that in August much of the north Atlantic is a source of CO₂ to the atmosphere, but north of a line between Ireland and Newfoundland it is a sink, and this sink may be enhanced by a high concentration of enzyme. The transfer velocity in the tropics also increases when the enzyme concentration rises, but this sea-air flux is more than compensated by an increased air-sea flux in the southern mid-latitudes.

The twelve maps in figure 9-21 show all four seasons February, May, August and November (from top to bottom). They compare the transfer velocities due to chemical enhancement for the "chlorophyll-only" enzyme distribution (left column) with the "high cost" physiological enzyme distribution (centre column), both for a global average enzyme concentration of 3.32nM. The corresponding CO₂ fluxes calculated with the "high cost" physiological distribution are shown in the right hand column. The colourscales are all the same (note that grey and white patches in the oceans are off the positive and negative ends of the colourscales respectively). All these maps include the effect of uncatalysed chemical enhancement, which is mainly in the tropics, and can also be identified by looking at the equivalent maps without enzyme (kd2, fd2, kd8 and fd8) which were shown earlier in figure 9-10 .

Comparing the maps in the left and centre columns, at first sight it seems that the "high cost" physiological distribution favours the high-pCO₂ tropics rather than the low-pCO₂ high latitudes, yet we know that the net global air-sea CO₂ flux is much greater using the "high-cost" physiological distribution. However, this overall appearance can be deceptive, we should consider the detail. While it is true that the physiological model has removed all of the enzyme from the cold winter polar seas, where even the catalysed reaction is too slow to be useful in aiding CO₂ uptake by the cells, its overall effect is to shift the balance of the enzyme distribution from the winter to the summer hemisphere, and from the Eastern to the Western equatorial pacific, and therefore in favour of low-pCO₂ regions. The highest concentrations are in the waters around the Indonesian archipelago which, although warm, are generally a sink for atmospheric CO₂ according to this Hamburg carbon cycle model. This can be seen from the CO₂ flux maps in the right hand column.

Notice in the Indian Ocean, for example, how wherever there is a patch of blue in the flux map, corresponding to air-sea CO₂ flux, there is a corresponding shift of enzyme towards this region and away from the yellow regions of sea-air CO₂ flux. In February in November, the physiological distribution allocates a lot of enzyme to the low-pCO₂ waters of the Kuroshio current off Japan and the Gulf Stream, whereas in August it removes enzyme from the high-pCO₂ north Atlantic and north Pacific and puts it instead in the South Atlantic and South-West Pacific, particularly around New-Zealand.

We should bear in mind that the distribution of CO₂ fluxes in the equatorial Pacific might be completely different in an El Niño year, which should be investigated in future work on this topic, especially since El Niño seems to be occurring more frequently in recent years. This was also discussed in section 1.3.6.

If the flux maps for the "high cost" physiological distribution are redrawn with the colourscale representing a much wider range of values, a few extremely high values would be apparent in the northernmost latitudes (70^o-80^o) in May, and just a little further south in October. The equivalent map for the "chlorophyll only" distribution shows the highest air-sea CO₂ fluxes in similar locations but in July. These wider colourscales render the rest of the map almost uniform, so they were not used on the maps shown here.

The six monthly latitude-band summary plots of the transfer velocity due to enhancement, shown in figure 9-22 , also compare these two distributions at three different average enzyme concentrations. The top row shows the "chlorophyll only" distribution and the bottom row the "high cost" physiological distribution, while the concentrations increase from 0.21nM (left) to 3.32 nM (centre) to 53.2 nM (right). The colourscales in the summary plots are roughly comparable between the two distributions, but different between the concentrations, since the average enzyme concentration on the right is 256 times higher than on the left. Nevertheless it is clear that the "chorophyll only" distribution concentrates the enzyme especially in the high northern latitudes (north of 50^o) in summer, whereas the "physiological distribution" puts more enzyme in the mid-latitudes (between 20^o and 50^o) in the winter months, although there are a few "hotspots" in the north. In winter these mid latitude regions have low pCO₂, but it is warmer and not so windy as in the polar seas, so the enzyme effect on the net global air-sea CO₂ flux due to enhancement is much greater for the "high cost" physiological distribution than for the chlorophyll distribution as observed from the global totals.

What about the "low cost" physiological distribution? The equivalent maps for August for the transfer velocity and CO₂ flux due to chemical enhancement, again with 3.23 nM average enzyme concentration, are shown in figure 9-23 . Although there are subtle differences they look very similar to the "chlorophyll only" distribution. The corresponding summary monthly latitude-band plots also shown in figure 9-23 indicate that the key difference is in the northern high-latitudes, where some very high enzyme concentrations must be found. Note that these extreme values caused rather skewed colourscales to be applied to the monthly latitude-band plot of the flux. Therefore, the summary monthly latitude band plot with a much lower average enzyme concentration is also shown (bottom right of figure 9-23 ).

9.7.3 Overall scale of enzyme catalysis effect

The initial aim of this research was to investigate the possibility that catalysis of chemical enhancement by Carbonic Anhydrase enzyme produced by marine algae in the sea-surface microlayer might sufficiently increase the air-sea exchange rate of CO₂ compared to inert trace gases, so as to explain the discrepancy between the global average transfer velocity based on experiments in lakes and wind tunnels (represented by the Liss and Merlivat parameterisation), and the higher figure calculated from the global ¹⁴C budget. It is fairly straightforward to extrapolate the curves of global average transfer velocity as a function of enzyme concentration, to find out how much enzyme would be needed in the microlayer to resolve this discrepancy. However we should also calculate the effect of this amount of enzyme on the net global air-sea flux of ¹²CO₂, which might be quite different from its effect on the global average transfer velocity, due to the intercorrelation between the catalysis effect and the pCO₂ distribution (as first suggested in Section 3.3 and apparent from the discussion of distribution effects in this chapter).

The results of such calculations are summarised in table 9-5below. For each combination of calculation options, the extrapolation has been made twice, either to bring the global average transfer velocity calculated with the Liss and Merlivat parameterisation to reach either 5.3 x10^-2 mol m^-2yr ^-1matm^-1, which is the global average unenhanced transfer velocity predicted by the Wanninkhof parameterisation without Rayleigh splitting, or alternatively to reach 6.2 x10^-2 mol m^-2yr ^-1matm^-1, which is the figure predicted by the global ¹⁴C budget. The calculation of how much enzyme is needed to reach these two transfer velocities was done automatically in a spreadsheet, based on a straight line extrapolation between the values for the13.3nM and the 53.2nM average enzyme concentration for each scenario. Although the relationship between transfer velocity and concentration is clearly not linear, there is insufficient data at high enzyme concentrations to justify extending the polynomial fit curves beyond the real dataset. A similar linear extrapolation was then used to estimate the net-global air-sea CO₂ flux expected with this average enzyme concentration, using the line corresponding to the appropriate set of calculation options.

The table shows that to reach the global average transfer velocity derived from the Carbon-14 budget, the average enzyme concentration in the microlayer needs to be in the range 78-137nM, slightly higher than the figure of 60nM predicted by the crude calculation presented earlier in Section 3.3 . However we must remember that the global average windspeed of this dataset (7.0 ms^-1) is lower than the figure used earlier (7.4 ms^-1), and used by Wanninkhof (1992) to derive his parameterisation. The amount of enzyme needed to bring the global average transfer velocity calculated with the Liss and Merlivat parameterisation (without Rayleigh splitting) to meet that calculated with the Wanninkhof parameterisation (i.e. to 5.3 x10^-2 mol m^-2yr ^-1matm^-1) is less: 64 -86nM, closer to the prediction made earlier.

The amount of enzyme needed is lowest for the "low cost" physiological distribution and highest for the "high cost" distribution, due to the "competition effect" discussed earlier, yet each mole of enzyme has a much greater effect on the net global air-sea CO₂ flux in the "high cost" distribution. Consequently the percentage increase in the net global air-sea CO₂ flux caused by adding enough enzyme to reconcile the global average transfer velocity with the ¹⁴C budget, is much greater for the "high cost" distribution, ranging from 127% to 202%, whereas the equivalent range for the "low cost" distribution is 48% to 71% and for the "chlorophyll only" distribution it is only 33% -43%.

The highest net global air-sea CO₂ flux reached using the "high cost" physiological distribution (and without Rayleigh splitting or faster OH^- reaction rate) is 5.65 Gt C yr^-1, compared to 1.87 Gt C yr^-1 without enzyme, clearly a dramatic change and well beyond the range of "missing Carbon" in the global carbon budget. In this case the effect on the net global air-sea CO₂ flux (202% increase) is greater than on the global average transfer velocity (94% increase). This seems to confirm the prediction made in Section 3.3 that catalysis by carbonic anhydrase would have a disproportionate effect on the net global air-sea flux of ¹²CO₂ compared to its effect on the net global air-sea flux of ¹⁴CO₂. The effect on the latter is assumed to be the same as the effect on the transfer velocity, since this one-way flux is almost independent of water pCO₂.

However using different calculation options the reverse can be shown: for example with the "chlorophyll only" distribution and the Rayleigh splitting of weekly winds the increase in the net global air-sea CO₂ flux (of Carbon-12) is only 33% but the increase in the net global air-sea flux of Carbon-14 (or global average transfer velocity) is 63%. Comparing the slopes of the curves of CO₂ flux and transfer velocity as a function of average enzyme concentration (bearing in mind that the scales don't start from the origin), it can be seen that the effect of enzyme on the global average transfer velocity is often greater than its effect on the net global air-sea CO₂ flux. This seems to contradict the prediction made in Section 3.3 , and the more sophisticated calculation presented here, which may help to explain the lower overall impact of the enzyme in the calculations presented in this chapter.

One such problem is the absence of DpCO₂ data derived from the carbon-cycle model for many of the coastal regions -particularly around the Indonesian Archipelago, and in the Red, Baltic, Mediterranean, East China and Japan Seas, which show as white areas on the CO₂ flux maps. In these areas DpCO₂ was assumed to be zero, and the water pCO₂ for calculating the carbonate speciation was therefore 360ppm. Therefore these areas were included in all the calculations and enzyme distributions, and influence the global average transfer velocity, but they do not count in the calculation of the net global air-sea CO₂ flux. This was not a great problem for the early calculations without any enzyme catalysis, since calculation from the dataset showed that these areas cover only 5.0% of the total surface area of the oceans. However a later calculation showed that with the "chlorophyll only" distribution, 15.6% of the enzyme was in the areas where DpCO₂ was zero, and with the "high cost" physiological distribution 17.6% of the enzyme was in these areas. Because these are mostly fairly warm areas of the ocean, compared to the polar seas where much of the rest of the chlorophyll is found, the proportion of the enzyme catalysis (catalysed CO₂ hydration rate constant) in the DpCO₂ = 0 areas was slightly higher - 17.5% for the "chlorophyll only" and 25.6% for the "high cost" physiological distribution.

In the light of these figures, it might be sensible to recalculate all the results with enzyme catalysis, excluding enzyme from all areas where DpCO₂ is zero, and see how this affects the net-global air-sea CO₂ fluxes. However this would require billions of calculations (see Section 9.5.1 ) which would take several more weeks, and we can guess the overall effect easily. So far as the CO₂ fluxes are concerned, all that would change is the average enzyme concentration corresponding to each net global air-sea CO₂ flux, so, for example, the curve for the "high cost physiological distribution" as a function of enzyme concentration would shift left towards the origin by about 17.6%. Since these coastal regions are not remarkable in terms of windspeed and temperature (on the 1 degree grid scale of this dataset), redistributing the enzyme from the coastal regions into other areas of the ocean would probably not have a great influence on the global average transfer velocity. Thus excluding enzyme from these areas might increase the net global air-sea CO₂ flux (Carbon-12) by a few percent, whereas it should have little effect on the global average transfer velocity (Carbon-14 flux).

Another reason for the smaller effect of both the physiologically-distributed enzyme catalysis and the OH^- reaction pathway in these calculations, is the narrower range of pCO₂ used here compared to the that used in Section 3.3 . If, instead of calculating the net global air-sea CO₂ flux, we calculate the absolute sum of all local air-sea and sea-air CO₂ fluxes (counting both directions as positive) we get a figure of 3.275 Gt C yr^-1 for the Liss and Merlivat parameterisation without enhancement or Rayleigh splitting, and 3.417 Gt C yr^-1 with enhancement. The equivalent net flux figures are 1.905 Gt C yr^-1 unenhanced, and 1.869 Gt C yr^-1 enhanced. Thus, although the absolute sum of all the local air-sea CO₂ fluxes is indeed much larger than the net flux, the difference is not so great as assumed earlier, and much smaller than the ratio of 50:1 assumed by Keller (1994) (see Section 1.3.8 ). This calculation also showed that half of the absolute sum of the local fluxes is found north of latitude 25^o N, due mainly to the low pCO₂ and high winds in the North Atlantic which is the largest sink for atmospheric CO₂.

We must also remember when looking at the effect of the physiological distribution on the net global air-sea CO₂ flux due to enzyme catalysis, that the calculation in Section 3.3 had a different baseline. In that case the physiological distribution was compared to a uniform enzyme distribution, whereas here all the enzyme distributions are based on the chlorophyll data, i.e. the physiology determines "CA per cell" but the chlorophyll determines "cells per litre". In this case the enzyme distribution is already biased towards low CO₂ areas of the ocean before any physiology is applied, so the relative effect of the physiology is smaller.

Finally, some words of caution about the interpretation of all the calculations presented in this chapter. Firstly, the physiological model depended on arbitrary constants used to determine the amount of CA per cell available in the microlayer as a function of the chlorophyll concentration measured by the CZCS satellite. To achieve the required global average enzyme concentrations further arbitrary scaling factors were used. Although it seems from the results discussed earlier that the effect of each mole of enzyme on the net global air-sea CO₂ flux is much greater for the "high cost" physiological distribution compared to the "low cost" distribution, the physiological model also suggested that if the "cost" of producing enzyme was so high, the concentration of enzyme produced by the phytoplankton would actually be several orders of magnitude lower than in the "low cost" scenario (see figures in the methods section). As the constants are arbitrary we cannot rule out either scenario, but it makes sense to assume that if the cost of producing enzyme is higher, there will be less of it overall.

Moreover the carbon cycle model used to derive the pCO₂ data is dependent on its boundary conditions, including the air-sea CO₂ flux. We have already noted that the model is calibrated to work with the Liss and Merlivat parameterisation and therefore overestimates the net global air-sea CO₂ flux when using the Wanninkhof parameterisation. The same overestimation would occur if there is a very large effect of enzyme catalysis. In the real world, if the gas exchange rate were enhanced by enzyme catalysis, the surface mixed layer would equilibrate faster with the atmosphere and the air-sea pCO₂ differences would therefore be smaller.

Most importantly, we must always bear in mind that the datasets used here are derived from several different sources and from several different years, and therefore this calculation does not take into account any short timescale intercorrelation between the pCO₂, windspeed, temperature and chlorophyll. This applies not only to local variability within the 1 degree resolution of the grid, but on the global scale wherever intercorrelation is dependent on rapid processes which vary from year to year. For example the recent data from the CARIOCA automated buoys showed how pCO₂ rose dramatically during storms, due to the waves deepening the mixed layer, and many measurements reported in the literature have shown how pCO₂ falls dramatically during algal blooms (see Section 1.3.3 ). To include the effect of such intercorrelations would require global datasets of all the parameters measured simultaneously. Perhaps such datasets may be available in the future.

I hope that the calculations in this chapter have demonstrated, above all, the importance of considering such intercorrelations between the factors which control the chemical enhancement of air-sea CO₂ exchange, both with and without enzyme catalysis, and that this will encourage others, when making similar calculations in the future, to experiment with combinations of different distributions of these parameters rather than using averages, since we will always be constrained by the lack of perfect datasets. Some more general thoughts regarding intercorrelation between all the parameters influencing gas exchange, will be discussed further in the final chapter, where some of the key results from this chapter will also be summarised.

Continue to Chapter 10:
Summary, Conclusions and Future Work

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